Remove the fuel inlet line to the carb and plug. Start engine up and run until the gas is out of the carb (engine will die). Re-install fuel line to carb (making sure it is clean) and crank over until it re-starts.
The intent of this excersize is to remove the small amount of debris that may be stuck between the needle and seat. From what I read, this drip developed right after you took off the fuel line and hooked it back up. This would indicate that the crap/debris was most likely introduced by you.
So remove it again but plug and run out of fuel. The incoming rush of fuel into the bowl(s) will most likely flush out the debris from the needle and seat, and it will be working properly.
Worth a try...it costs nothing and can be very sucessful and time/money saving.

Good advice but I'm not sure how you can plug a fuel line that is under pressure with the engine running. I can envision gas spraying everywhere. You can accomplish the same thing by just removing one of the bottom screws holding the float bowl on and letting it drain. I just cut a pop can down with a utility knife to make a small container to drain it into.

You could also try removing the fuel line and spraying some compressed air into the bowl once it has been drained.